What is a Function Notation

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What does "Function Notation" mean?

The function notation is a simple and efficient way to write functions, making them easy to write, understand, and evaluate. It uses algebraic expressions to summarize how a function affects the input value to get the desired output value. The relationship between the input and output values is shown by the function \(f(x)\), read as "\(f\) of \(x\)".

How do you evaluate the values of a function notation?

When evaluating function notations for a specific input value, substitute the input value into the algebraic expression that defines the function. When figuring out the value of a function notation, the focus is on one input and the output that goes with it.

Look at the function shown above. When evaluating \(f(x) \ = \ 2x \ + \ 7\) at \(x \ = \ 9\), substitute the given input value to evaluate and find the value of \(f(9)\).
\(f(x) \ = \ 2(9) \ + \ 7 \ = \ 18 \ + \ 7 \ = \ 25\)

Function Notation

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Exercises for Function Notation

1) \(p(s) = 4s \ + \ 2\), find \(p(8) \)\(\ \Rightarrow \ \)

2) \(f(x) = 6x^2 \ + \ x \ + \ 2\), find \(f(2) \)\(\ \Rightarrow \ \)

3) \(f(x) = 11x^2 \ - \ x \ + \ 2\), find \(f(4) \)\(\ \Rightarrow \ \)

4) \(g(t) = 2t^2 \ + \ 3\), find \(g(9) \)\(\ \Rightarrow \ \)

5) \(p(s) = 9s^2 \ + \ 4\), find \(p(3) \)\(\ \Rightarrow \ \)

6) \(m(u) = 10u^2 \ + \ 2\), find \(m(6) \)\(\ \Rightarrow \ \)

7) \(p(s) = 4s^2 \ - \ s \ + \ 9\), find \(p(9) \)\(\ \Rightarrow \ \)

8) \(g(t) = 7t^2 \ + \ t \ + \ 7\), find \(g(6) \)\(\ \Rightarrow \ \)

9) \(m(u) = 5u \ + \ 3\), find \(m(2) \)\(\ \Rightarrow \ \)

10) \(f(x) = 6x \ + \ 7\), find \(f(8) \)\(\ \Rightarrow \ \)

Answers

1) \(p(s) = 4s \ + \ 2\), find \(p(8) \)\(\ \Rightarrow \ \color{red}{p(8) = 34}\)

Solution
Substitute \(8\) for (s) and solve it: \( p(8) = 4(8) + 2 = 4 \times 8 + 2 = 32 + 2 = 34\)

2) \(f(x) = 6x^2 \ + \ x \ + \ 2\), find \(f(2) \)\(\ \Rightarrow \ \color{red}{f(2) = 28}\)

Solution
Substitute \2\ for (x) and solve it: \(f(2) = 6 \times 2 ^2 + 2 + 2 = 28 \)

3) \(f(x) = 11x^2 \ - \ x \ + \ 2\), find \(f(4) \)\(\ \Rightarrow \ \color{red}{f(4) = 174}\)

Solution
Substitute \4\ for (x) and solve it: \(f(4) = 11 \times 4 ^2 - 4 + 2 = 174 \)

4) \(g(t) = 2t^2 \ + \ 3\), find \(g(9) \)\(\ \Rightarrow \ \color{red}{g(9) = 165}\)

5) \(p(s) = 9s^2 \ + \ 4\), find \(p(3) \)\(\ \Rightarrow \ \color{red}{p(3) = 85}\)

6) \(m(u) = 10u^2 \ + \ 2\), find \(m(6) \)\(\ \Rightarrow \ \color{red}{m(6) = 362}\)

7) \(p(s) = 4s^2 \ - \ s \ + \ 9\), find \(p(9) \)\(\ \Rightarrow \ \color{red}{p(9) = 324}\)

8) \(g(t) = 7t^2 \ + \ t \ + \ 7\), find \(g(6) \)\(\ \Rightarrow \ \color{red}{g(6) = 265}\)

9) \(m(u) = 5u \ + \ 3\), find \(m(2) \)\(\ \Rightarrow \ \color{red}{m(2) = 13}\)

10) \(f(x) = 6x \ + \ 7\), find \(f(8) \)\(\ \Rightarrow \ \color{red}{f(8) = 55}\)

What is a Function Notation